Finite Group Databasebeta

← #35412862

Subgroups — #35412862

Order 21248.

1062 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128079C211yesmaximal, characteristic
2C2×#19127809C211yesmaximal, characteristic
3C2×#19127806C212yesmaximal
4C4×#14581790C212yesmaximal
5#24908335C211yesmaximal, characteristic
6#24908332C211yesmaximal, characteristic
7#24908331C212yesmaximal
8#24908263C212yesmaximal
9#24907618C211yesmaximal, characteristic
10#97×Dic83C211yesmaximal, characteristic
11C2×#441×C83C211yesmaximal, characteristic
12C22×Dic332C2211yescharacteristic
13C22×#13050580C2212yes—
14C2×#14581790C2212yes—
15C2×C4×Dic166C2212yes—
16#19128079C418yescomplemented
17#19127809—24no—
18#19127806—28no—
19C2×#14581724C2211yescharacteristic
20C2×#14581723C2212yes—
21C2×#14581717C2212yes—
22C2×#14581716C2212yes—
23C2×#14581715C2212yes—
24C2×#14581703C2211yescharacteristic
25C2×#14581702C2211yescharacteristic
26C2×#14581702C2211yescharacteristic
27C2×C8×Dic83C2211yescharacteristic
28C2×C8×Dic83C2211yescharacteristic
29#19127608C2212yes—
30#19127606C2212yes—
31#19127596—24no—
32#19127570C2212yes—
33C4×Dic83⋊C4—24no—
34C42×Dic83C2211yescharacteristic
35C22×Q16×C83C2211yescharacteristic
36C2×C4×Q8×C83C2212yes—
37#441×C83—24no—
38C2×#106×C83C2211yescharacteristic
39C2×#103×C83C2212yes—
40C2×#97×C83C2211yescharacteristic
41C22×Dic166C2312yes—
42C2×Dic332—22no—
43C2×Dic332—22no—
44C2×Dic332C2×C414yes—
45C2×#13050580—24no—
46C2×#13050580—24no—
47C2×#13050580C2×C418yes—
48C22×C83⋊C8C2311yescharacteristic
49C22×C83⋊C8C2311yescharacteristic
50#14581790—24no—
51#14581790C2×C418yes—
52C4×Dic166—24no—
53C4×Dic166—24no—
54C2×C4⋊Dic83C2312yes—
55C2×Dic83⋊C4—24no—
56C2×Dic83⋊C4—24no—
57C2×Dic83⋊C4—22no—
58C2×C4×Dic83—22no—
59C2×C4×Dic83D414yes—
60C2×C4×Dic83C2311yescharacteristic
61C2×C4×Dic83C2311yescharacteristic
62#14581724—22no—
63#14581723—24no—
64#14581717—24no—
65#14581716—24no—
66#14581715—24no—
67#14581703D414yes—
68#14581702—22no—
69#14581702—22no—
70C8×Dic83—22no—
71C8×Dic83C2×C414yes—
72C83⋊#95—24no—
73C83⋊#95—24no—
74C22×Q8×C83C2312yes—
75C2×Q16×C83—22no—
76C2×Q16×C83—22no—
77C2×Q16×C83C2×C414yes—
78C22×C8×C83C2311yescharacteristic
79C22×C8×C83C2311yescharacteristic
80C4×Q8×C83—24no—
81C4×Q8×C83—24no—
82C2×C4⋊C4×C83—22no—
83C2×C4⋊C4×C83C2312yes—
84C2×C42×C83—22no—
85C2×C42×C83C2311yescharacteristic
86#106×C83—22no—
87#103×C83—24no—
88#97×C83D414yes—
89C2×Dic166—22no—
90C2×Dic166—22no—
91C2×Dic166—22no—
92C2×Dic166—22no—
93C2×Dic166—22no—
94C2×Dic166C22×C414yes—
95C22×Dic83—22no—
96C22×Dic83—22no—
97C22×Dic83C2×D412yes—
98C22×Dic83C2×D412yes—
99Dic332—28no—
100#13050580—216no—
101C2×C83⋊C8—21no—
102C2×C83⋊C8—21no—
103C2×C83⋊C8C22×C412yes—
104C2×C83⋊C8C2×D412yes—
105C2×C83⋊C8C2×D412yes—
106C2×C83⋊C8#4112yes—
107C4⋊Dic83—22no—
108C4⋊Dic83—22no—
109Dic83⋊C4—216no—
110Dic83⋊C4—44no—
111Dic83⋊C4—48no—
112C4×Dic83—21no—
113C4×Dic83—21no—
114C4×Dic83—28no—
115C4×Dic83—44no—
116C4×Dic83C22×C412yes—
117C4×Dic83#4112yes—
118C2×Q8×C83—22no—
119C2×Q8×C83—22no—
120C2×Q8×C83—22no—
121C2×Q8×C83—22no—
122C2×Q8×C83—22no—
123C2×Q8×C83C22×C414yes—
124C22×C4×C83—22no—
125C22×C4×C83—22no—
126C22×C4×C83C2×D412yes—
127C22×C4×C83C2411yescharacteristic
128Q16×C83—28no—
129C2×C8×C83—21no—
130C2×C8×C83—21no—
131C2×C8×C83C22×C412yes—
132C2×C8×C83C2×D412yes—
133C2×C8×C83C2×D412yes—
134C2×C8×C83#4112yes—
135C4⋊C4×C83—22no—
136C4⋊C4×C83—22no—
137C4⋊C4×C83—44no—
138C42×C83—44no—
139C42×C83C2×D412yes—
140C42×C83C2×D412yes—
141C23×C83C22×D411yescharacteristic
142Q8×C83—24no—
143Q8×C83—24no—
144Q8×C83—42no—
145Q8×C83—42no—
146C2×C4×C83—24no—
147C2×C4×C83—24no—
148C2×C4×C83—42no—
149C2×C4×C83—42no—
150C2×C4×C83—42no—
151C2×C4×C83—44no—
152C2×C4×C83#12714yes—
153C2×C4×C83C23×C411yescharacteristic
154C2×C4×C83C22×D411yescharacteristic
155C2×C4×C83C22×D411yescharacteristic
156C2×C4×C83C2×#4111yescharacteristic
157C2×C4×C83C2×#4111yescharacteristic
158C2×C4×C83C2×#4111yescharacteristic
159C2×Dic83—24no—
160C2×Dic83—22no—
161C2×Dic83—24no—
162C2×Dic83—42no—
163C2×Dic83—42no—
164C2×Dic83—42no—
165C2×Dic83—44no—
166C2×Dic83C4×D414yes—
167C2×Dic83#13718yes—
168Dic166—24no—
169Dic166—24no—
170Dic166—42no—
171Dic166—42no—
172C8×C83—22no—
173C8×C83C4×D414yes—
174C83⋊C8—22no—
175C83⋊C8C4×D414yes—
176C22×C83C2×C4×D411yescharacteristic
177C22×C83C2×#12711yescharacteristic
178C22×C83#53211yescharacteristic
179C22×C83C2×#13714yes—
180C4×C83—24no—
181C4×C83—44no—
182C4×C83—82no—
183C4×C83C2×C4×D411yescharacteristic
184C4×C83C2×C4×D411yescharacteristic
185C4×C83#53211yescharacteristic
186C4×C83#53211yescharacteristic
187Dic83—44no—
188Dic83—42no—
189Dic83—82no—
190Dic83#44118yescomplemented
191#21691—831nomaximal, Sylow
192C2×C83C4×#12711yescharacteristic
193C2×C83C2×#44112yes—
194C2×C83#315212yes—
195C2×C83#318512yes—
196C2×#494—831no—
197C2×#441—831no—
198C2×#441—832no—
199C2×#441D8311yescharacteristic
200C4×C4⋊Q8—832no—
201#1971—831no—
202#1971—832no—
203#1971—831no—
204#1956—832no—
205#1844—831no—
206C4×#97—831no—
207C83#2169111yescharacteristic, complemented, Sylow
208C22×Q16—832no—
209C22×Q16—831no—
210C22×Q16C2×D8311yescharacteristic
211C2×C4⋊Q8—832no—
212C2×C4×Q8—832no—
213C2×C4×Q8C2×D8312yes—
214#494—838no—
215#441—24no—
216#441—1668no—
217#441—1664no—
218C2×#106—831no—
219C2×#106—832no—
220C2×#106C2×D8311yescharacteristic
221C2×#103—832no—
222C2×#103—832no—
223C2×#103—832no—
224C2×#103C2×D8312yes—
225C2×#97—831no—
226C2×#97—831no—
227C2×#97—831no—
228C2×#97C2×D8311yescharacteristic
229C2×C4×C8—831no—
230C2×C4×C8—831no—
231#391—832no—
232#391—832no—
233#389—1664no—
234#384—832no—
235C4×C4⋊C4—1664no—
236C43—831no—
237C22×Q8—832no—
238C22×Q8C22×D8312yes—
239C2×Q16—22no—
240C2×Q16—22no—
241C2×Q16—838no—
242C2×Q16—834no—
243C2×Q16—1664no—
244C2×Q16—1664no—
245C2×Q16—1662no—
246C2×Q16—1662no—
247C2×Q16C4×D8314yes—
248C22×C8—831no—
249C22×C8—831no—
250C22×C8C22×D8311yescharacteristic
251C22×C8C22×D8311yescharacteristic
252C4⋊Q8—838no—
253C4⋊Q8—1664no—
254C4×Q8—24no—
255C4×Q8—24no—
256C4×Q8—1664no—
257C4×Q8—1664no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—832no—
260C2×C4⋊C4—1664no—
261C2×C4⋊C4—1662no—
262C2×C4⋊C4—1664no—
263C2×C4⋊C4C22×D8312yes—
264C2×C42—22no—
265C2×C42—831no—
266C2×C42—834no—
267C2×C42—831no—
268C2×C42—1662no—
269C2×C42C22×D8311yescharacteristic
270#106—22no—
271#106—1664no—
272#106—1662no—
273#103—24no—
274#103—1664no—
275#103—1664no—
276#103—1664no—
277#97—834no—
278#97—1662no—
279#97—1662no—
280#97C22⋊D8314yes—
281C4×C8—834no—
282C4×C8—1662no—
283#95—1664no—
284#95—1664no—
285C2×Q8—22no—
286C2×Q8—22no—
287C2×Q8—22no—
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8—834no—
291C2×Q8—1662no—
292C2×Q8—1662no—
293C2×Q8—1662no—
294C2×Q8—1662no—
295C2×Q8—1662no—
296C2×Q8C2×C4×D8314yes—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—832no—
300C22×C4—832no—
301C22×C4—1662no—
302C22×C4—1662no—
303C22×C4D4×D8312yes—
304C22×C4C23×D8311yescharacteristic
305Q16—28no—
306Q16—16616no—
307Q16—1668no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—832no—
311C2×C8—832no—
312C2×C8—832no—
313C2×C8—832no—
314C2×C8—1661no—
315C2×C8—1661no—
316C2×C8C2×C4×D8312yes—
317C2×C8C2×C22⋊D8312yes—
318C2×C8C2×C22⋊D8312yes—
319C2×C8#1305059012yes—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—44no—
323C4⋊C4—3328no—
324C4⋊C4—3324no—
325C4⋊C4—16616no—
326C4⋊C4—1662no—
327C4⋊C4—1662no—
328C42—44no—
329C42—3324no—
330C42—832no—
331C42—832no—
332C42—1668no—
333C42—1661no—
334C42—1661no—
335C42D4×D8312yes—
336C42C2×C22⋊D8312yes—
337C23C2×D4×D8311yescharacteristic
338Q8—24no—
339Q8—24no—
340Q8—42no—
341Q8—42no—
342Q8—3322no—
343Q8—3322no—
344Q8—1664no—
345Q8—1664no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—3322no—
353C2×C4—3322no—
354C2×C4—3324no—
355C2×C4—3322no—
356C2×C4—834no—
357C2×C4—838no—
358C2×C4—1664no—
359C2×C4—1664no—
360C2×C4—1662no—
361C2×C4#1458178814yes—
362C2×C4C22×C4×D8311yescharacteristic
363C2×C4C2×D4×D8311yescharacteristic
364C2×C4C22×C22⋊D8311yescharacteristic
365C2×C4#41×D8311yescharacteristic
366C2×C4#41×D8311yescharacteristic
367C2×C4C2×#1305059011yescharacteristic
368C8—22no—
369C8—834no—
370C8—1662no—
371C8C4×C22⋊D8314yes—
372C22C4×D4×D8311yescharacteristic
373C22C2×#1458178811yescharacteristic
374C22#1912824811yescharacteristic
375C22#137×D8314yes—
376C4—24no—
377C4—44no—
378C4—82no—
379C4—3322no—
380C4—3324no—
381C4—838no—
382C4—6642no—
383C4C4×D4×D8311yescharacteristic
384C4C2×C4×C22⋊D8311yescharacteristic
385C4#1912824711yescharacteristic
386C4#1912824811yescharacteristic
387C2C4×#1458178811yescharacteristic
388C2#441×D8312yes—
389C2#2491791812yes—
390C2#2491820512yes—
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×#441×C83C2
socle, prime radicalC23×C83C22×D4
cosocleC22×C4×C83C24
hypercenterC2×#441D83
hypocenterC83#21691
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
16. #19128079C4semidirect
190. Dic83#441semidirect
207. C83#21691semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191280792
C2×#191278092
C2×#191278062
C4×#145817902
#249083352
#249083322
#249083312
#249082632
#249076182
#97×Dic832
C2×#441×C832
#2169183